Prove that for each positive integer
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
there exist
![n](/media/m/a/e/5/ae594d7d1e46f4b979494cf8a815232b.png)
consecutive positive integers none of which is an integral power of a prime number.
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Prove that for each positive integer $n$ there exist $n$ consecutive positive integers none of which is an integral power of a prime number.